Problem 2582. Cut an orange

Created by Jan Orwat

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Inspired by problem</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2175\"><w:r><w:t>2175</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A hungry matlab enthusiast has an orange. He decides to cut it into pieces using three dimensional grid.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given grid density</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> please help him to find the number of ideal cubes full of juicy orange and the number of pieces containing also some peel.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example: For</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N=3</w:t></w:r><w:r><w:t> matlab enthusiast is not satisfied. He gets [1 26]. Only one cube and 26 unpeeled pieces!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Related problems:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/554\"><w:r><w:t>554</w:t></w:r></w:hyperlink><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1283\"><w:r><w:t>1283</w:t></w:r></w:hyperlink><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/1387\"><w:r><w:t>1387</w:t></w:r></w:hyperlink></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

76 Solutions
20 Solvers

Last Solution submitted on Apr 01, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Alfonso Nieto-Castanon on 8 Oct 2014

Perhaps I am misinterpreting, but it seems to me that some of your testsuite solutions are incorrect. For example, for N=5 I seem to be getting 19 instead of 27 cubes entirely within the sphere. I double-check using this code: x=rand(1e6,3); r=sum((x-.5).^2,2)

Jan Orwat on 8 Oct 2014

You are totally right. I've generated answers using my solution, which was wrong. My fault is I haven't examined it any other way. Considering N=5, there could fit inside the sphere only a 3x3x3 cube, but its space diagonal is 3*sqrt(3) which is bigger than 5, the diameter of sphere. So, there cannot be more than 27-8=19 cubes inside. Thanks, for pointing that out, Alfonso!

Jan Orwat on 8 Oct 2014

Fixed & rescored now. It leads now to smaller-size answers. Consider the fact that for some N (for example 6) there are some quasi-cubes containing a very small amount of peel from those ultra-thin-peel-sweet-juicy-ideal-oranges ;-)

Problem Recent Solvers20

Problem Tags

orange sampling sphere

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2582. Cut an orange

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author40

Problem Tags

Community Treasure Hunt

Problem 2582. Cut an orange

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author40

Problem Tags

Community Treasure Hunt

Players